{
  "alt": "Two lines with confidence bands, vote-weighted and unweighted, for the correlation of spread with distance from an even split at six cutoffs of county margin. The unweighted line is negative at every cutoff and falls as more counties enter. The vote-weighted line is close to zero, with intervals that include zero, at cutoffs of {fact:cutoff_30}, {fact:cutoff_40} and {fact:cut_within} points, and is negative at wider cutoffs.",
  "caption": "Compare the two lines: the unweighted line stays below zero at every cutoff, while the vote-weighted line has an interval that includes zero up to a cutoff of {fact:cut_within} points and excludes it from {fact:cutoff_60} points up. A county enters a cutoff when the size of its margin is at or below it, so the last point uses every county. Vote-weighted counts each county in proportion to its two-party votes; unweighted counts each county once. The data table adds the correlations with county size fixed and with size and state fixed.",
  "data": [
    {
      "conf_high": 0.0826476,
      "conf_low": -0.12661,
      "cutoff": 30,
      "estimate": -0.0246649,
      "n": 954,
      "no_controls": "−0.02 [−0.13, +0.08]",
      "series": "Vote-weighted",
      "size_fixed": "+0.01 [−0.09, +0.10]",
      "size_state_fixed": "−0.07 [−0.18, +0.02]"
    },
    {
      "conf_high": -0.0578857,
      "conf_low": -0.177378,
      "cutoff": 30,
      "estimate": -0.11945,
      "n": 954,
      "no_controls": "−0.12 [−0.18, −0.06]",
      "series": "Unweighted",
      "size_fixed": "−0.13 [−0.19, −0.07]",
      "size_state_fixed": "−0.17 [−0.23, −0.11]"
    },
    {
      "conf_high": 0.0364198,
      "conf_low": -0.176919,
      "cutoff": 40,
      "estimate": -0.0691889,
      "n": 1321,
      "no_controls": "−0.07 [−0.18, +0.04]",
      "series": "Vote-weighted",
      "size_fixed": "−0.03 [−0.13, +0.05]",
      "size_state_fixed": "−0.08 [−0.20, 0.00]"
    },
    {
      "conf_high": -0.144408,
      "conf_low": -0.251773,
      "cutoff": 40,
      "estimate": -0.199121,
      "n": 1321,
      "no_controls": "−0.20 [−0.25, −0.14]",
      "series": "Unweighted",
      "size_fixed": "−0.21 [−0.26, −0.15]",
      "size_state_fixed": "−0.25 [−0.30, −0.20]"
    },
    {
      "conf_high": 0.0843983,
      "conf_low": -0.181874,
      "cutoff": 50,
      "estimate": -0.0445753,
      "n": 1725,
      "no_controls": "−0.04 [−0.18, +0.08]",
      "series": "Vote-weighted",
      "size_fixed": "+0.01 [−0.12, +0.12]",
      "size_state_fixed": "−0.04 [−0.19, +0.06]"
    },
    {
      "conf_high": -0.21672,
      "conf_low": -0.303464,
      "cutoff": 50,
      "estimate": -0.260848,
      "n": 1725,
      "no_controls": "−0.26 [−0.30, −0.22]",
      "series": "Unweighted",
      "size_fixed": "−0.26 [−0.30, −0.21]",
      "size_state_fixed": "−0.31 [−0.36, −0.27]"
    },
    {
      "conf_high": -0.0431833,
      "conf_low": -0.26336,
      "cutoff": 60,
      "estimate": -0.150169,
      "n": 2156,
      "no_controls": "−0.15 [−0.26, −0.04]",
      "series": "Vote-weighted",
      "size_fixed": "−0.08 [−0.18, +0.03]",
      "size_state_fixed": "−0.11 [−0.24, −0.02]"
    },
    {
      "conf_high": -0.340596,
      "conf_low": -0.410541,
      "cutoff": 60,
      "estimate": -0.37646,
      "n": 2156,
      "no_controls": "−0.38 [−0.41, −0.34]",
      "series": "Unweighted",
      "size_fixed": "−0.36 [−0.39, −0.32]",
      "size_state_fixed": "−0.39 [−0.44, −0.35]"
    },
    {
      "conf_high": -0.133957,
      "conf_low": -0.339075,
      "cutoff": 70,
      "estimate": -0.23721,
      "n": 2593,
      "no_controls": "−0.24 [−0.34, −0.13]",
      "series": "Vote-weighted",
      "size_fixed": "−0.15 [−0.25, −0.04]",
      "size_state_fixed": "−0.20 [−0.33, −0.10]"
    },
    {
      "conf_high": -0.451575,
      "conf_low": -0.507411,
      "cutoff": 70,
      "estimate": -0.47986,
      "n": 2593,
      "no_controls": "−0.48 [−0.51, −0.45]",
      "series": "Unweighted",
      "size_fixed": "−0.44 [−0.47, −0.40]",
      "size_state_fixed": "−0.48 [−0.52, −0.45]"
    },
    {
      "conf_high": -0.195752,
      "conf_low": -0.392976,
      "cutoff": 100,
      "estimate": -0.291055,
      "n": 2853,
      "no_controls": "−0.29 [−0.39, −0.20]",
      "series": "Vote-weighted",
      "size_fixed": "−0.19 [−0.30, −0.09]",
      "size_state_fixed": "−0.25 [−0.37, −0.16]"
    },
    {
      "conf_high": -0.523794,
      "conf_low": -0.57113,
      "cutoff": 100,
      "estimate": -0.547169,
      "n": 2853,
      "no_controls": "−0.55 [−0.57, −0.52]",
      "series": "Unweighted",
      "size_fixed": "−0.49 [−0.52, −0.46]",
      "size_state_fixed": "−0.55 [−0.58, −0.52]"
    }
  ],
  "id": "ext_by_cutoff",
  "notes": [
    "The last cutoff, {fact:margin_max} points, includes every county, because no margin can be larger. The number in the tooltip is the number of counties in the row. Each interval resamples the counties of the row {fact:n_boot} times; a full count has no sampling error, so the interval says how much the correlation would move with a different set of counties."
  ],
  "source": "MIT Election Data and Science Lab, 2024 precinct-level presidential returns; county totals summed from the precincts; full counts of votes, not survey estimates, so nothing is weighted except by two-party votes where stated",
  "spec": {
    "annotations": [
      {
        "label": "No correlation",
        "type": "y-rule",
        "y": 0
      }
    ],
    "colors": {
      "Unweighted": "cat4",
      "Vote-weighted": "cat3"
    },
    "hi": "conf_high",
    "lo": "conf_low",
    "n": "n",
    "series": "series",
    "x": "cutoff",
    "xDomain": [
      30,
      100
    ],
    "xFormat": {
      "digits": 0
    },
    "xLabel": "Counties included: a margin of at most this many points",
    "y": "estimate",
    "yDomain": [
      -0.7,
      0.3
    ],
    "yFormat": {
      "digits": 2,
      "signed": true
    },
    "yLabel": "Correlation of spread with distance from an even split"
  },
  "subtitle": "Correlation between the spread of precinct margins and the size of the county margin, among counties with a margin at or below each cutoff, 2024, with 95% intervals",
  "table": {
    "columns": [
      {
        "key": "cutoff",
        "label": "Cutoff (points of margin)"
      },
      {
        "key": "series",
        "label": "Weighting"
      },
      {
        "format": {
          "digits": 0,
          "thousands": true
        },
        "key": "n",
        "label": "Counties"
      },
      {
        "key": "no_controls",
        "label": "No controls"
      },
      {
        "key": "size_fixed",
        "label": "Size fixed"
      },
      {
        "key": "size_state_fixed",
        "label": "Size and state fixed"
      }
    ]
  },
  "title": "Spread falls with distance from an even split, except in vote-weighted comparisons of counties within {fact:cut_within} points",
  "type": "line"
}